%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU314+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:18 PM UTC 2026
% Result : Theorem 1.18s 1.15s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 4
% Syntax : Number of formulae : 120 ( 8 unt; 2 def)
% Number of atoms : 752 ( 81 equ)
% Maximal formula atoms : 21 ( 6 avg)
% Number of connectives : 1082 ( 450 ~; 448 |; 167 &)
% ( 7 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 271 ( 203 !; 68 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f30,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X5 = X3
& closed_subset(X5,X0)
& subset(X1,X3) )
& X2 = X4
& ? [X6] :
( element(X6,powerset(the_carrier(X0)))
& X6 = X4
& closed_subset(X6,X0)
& subset(X1,X4) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,powerset(the_carrier(X0)))
& X4 = X3
& ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& X7 = X3
& closed_subset(X7,X0)
& subset(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
fof(f31,plain,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( ! [X2,X3,X4] :
( ( X2 = X3
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X5 = X3
& closed_subset(X5,X0)
& subset(X1,X3) )
& X2 = X4
& ? [X6] :
( element(X6,powerset(the_carrier(X0)))
& X6 = X4
& closed_subset(X6,X0)
& subset(X1,X4) ) )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X0)))
& X8 = X9
& ? [X10] :
( element(X10,powerset(the_carrier(X0)))
& X8 = X10
& closed_subset(X10,X0)
& subset(X1,X8) ) ) ) ) ),
inference(rectify,[],[f30]) ).
fof(f33,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f34,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( in(X3,X2)
<~> ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X0)))
& X8 = X9
& ? [X10] :
( element(X10,powerset(the_carrier(X0)))
& X8 = X10
& closed_subset(X10,X0)
& subset(X1,X8) ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X5 = X3
& closed_subset(X5,X0)
& subset(X1,X3) )
& X2 = X4
& ? [X6] :
( element(X6,powerset(the_carrier(X0)))
& X6 = X4
& closed_subset(X6,X0)
& subset(X1,X4) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f31]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X0)))
& X8 = X9
& ? [X10] :
( element(X10,powerset(the_carrier(X0)))
& X8 = X10
& closed_subset(X10,X0)
& subset(X1,X8) ) ) )
| ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X5 = X3
& closed_subset(X5,X0)
& subset(X1,X3) )
& X2 = X4
& ? [X6] :
( element(X6,powerset(the_carrier(X0)))
& X6 = X4
& closed_subset(X6,X0)
& subset(X1,X4) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f35]) ).
fof(f40,definition,
! [X0,X4,X1] :
( ? [X6] :
( element(X6,powerset(the_carrier(X0)))
& X6 = X4
& closed_subset(X6,X0)
& subset(X1,X4) )
| ~ sP0(X0,X4,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f41,definition,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X5 = X3
& closed_subset(X5,X0)
& subset(X1,X3) )
& X2 = X4
& sP0(X0,X4,X1) )
| ~ sP1(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X0)))
& X8 = X9
& ? [X10] :
( element(X10,powerset(the_carrier(X0)))
& X8 = X10
& closed_subset(X10,X0)
& subset(X1,X8) ) ) )
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(definition_folding,[],[f36,f41,f40]) ).
fof(f43,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| in(X3,X2) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f34]) ).
fof(f44,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| in(X3,X2) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) )
| ~ in(X3,X2) )
& ( ( in(X3,powerset(the_carrier(X0)))
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X3 = X5
& closed_subset(X5,X0)
& subset(X1,X3) ) )
| in(X3,X2) ) )
& topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
( ! [X2] :
( ( ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(sK2)))
| sK4(X2) != X4
| ~ closed_subset(X4,sK2)
| ~ subset(sK3,sK4(X2)) )
| ~ in(sK4(X2),X2) )
& ( ( in(sK4(X2),powerset(the_carrier(sK2)))
& element(sK5(X2),powerset(the_carrier(sK2)))
& sK4(X2) = sK5(X2)
& closed_subset(sK5(X2),sK2)
& subset(sK3,sK4(X2)) )
| in(sK4(X2),X2) ) )
& topological_space(sK2)
& top_str(sK2)
& element(sK3,powerset(the_carrier(sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4(X2)),skolemize(X5,sK5(X2))],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X5 = X3
& closed_subset(X5,X0)
& subset(X1,X3) )
& X2 = X4
& sP0(X0,X4,X1) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f41]) ).
fof(f48,plain,
! [X0,X1] :
( ( sK7(X0,X1) != sK8(X0,X1)
& sK6(X0,X1) = sK7(X0,X1)
& element(sK9(X0,X1),powerset(the_carrier(X0)))
& sK7(X0,X1) = sK9(X0,X1)
& closed_subset(sK9(X0,X1),X0)
& subset(X1,sK7(X0,X1))
& sK6(X0,X1) = sK8(X0,X1)
& sP0(X0,sK8(X0,X1),X1) )
| ~ sP1(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f47]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ~ in(X9,powerset(the_carrier(X0)))
| X8 != X9
| ! [X10] :
( ~ element(X10,powerset(the_carrier(X0)))
| X8 != X10
| ~ closed_subset(X10,X0)
| ~ subset(X1,X8) ) ) )
& ( ? [X9] :
( in(X9,powerset(the_carrier(X0)))
& X8 = X9
& ? [X10] :
( element(X10,powerset(the_carrier(X0)))
& X8 = X10
& closed_subset(X10,X0)
& subset(X1,X8) ) )
| ~ in(X8,X7) ) )
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f42]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| X3 != X5
| ~ closed_subset(X5,X0)
| ~ subset(X1,X3) ) ) )
& ( ? [X6] :
( in(X6,powerset(the_carrier(X0)))
& X3 = X6
& ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& X3 = X7
& closed_subset(X7,X0)
& subset(X1,X3) ) )
| ~ in(X3,X2) ) )
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK11(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ! [X5] :
( ~ element(X5,powerset(the_carrier(X0)))
| X3 != X5
| ~ closed_subset(X5,X0)
| ~ subset(X1,X3) ) ) )
& ( ( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
& sK12(X0,X1,X3) = X3
& element(sK13(X0,X1,X3),powerset(the_carrier(X0)))
& sK13(X0,X1,X3) = X3
& closed_subset(sK13(X0,X1,X3),X0)
& subset(X1,X3) )
| ~ in(X3,sK11(X0,X1)) ) )
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X6,sK12(X0,X1,X3)),skolemize(X7,sK13(X0,X1,X3))],[f53]) ).
fof(f56,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f46]) ).
fof(f57,plain,
top_str(sK2),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
topological_space(sK2),
inference(cnf_transformation,[],[f46]) ).
fof(f59,plain,
! [X2] :
( subset(sK3,sK4(X2))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f60,plain,
! [X2] :
( closed_subset(sK5(X2),sK2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f61,plain,
! [X2] :
( sK4(X2) = sK5(X2)
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f62,plain,
! [X2] :
( element(sK5(X2),powerset(the_carrier(sK2)))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f63,plain,
! [X2] :
( in(sK4(X2),powerset(the_carrier(sK2)))
| in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,plain,
! [X2,X4] :
( ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ~ element(X4,powerset(the_carrier(sK2)))
| sK4(X2) != X4
| ~ closed_subset(X4,sK2)
| ~ subset(sK3,sK4(X2))
| ~ in(sK4(X2),X2) ),
inference(cnf_transformation,[],[f46]) ).
fof(f66,plain,
! [X0,X1] :
( sK6(X0,X1) = sK8(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0,X1] :
( sK6(X0,X1) = sK7(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f72,plain,
! [X0,X1] :
( sK7(X0,X1) != sK8(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f77,plain,
! [X3,X0,X1] :
( subset(X1,X3)
| ~ in(X3,sK11(X0,X1))
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f78,plain,
! [X3,X0,X1] :
( closed_subset(sK13(X0,X1,X3),X0)
| ~ in(X3,sK11(X0,X1))
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f79,plain,
! [X3,X0,X1] :
( sK13(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f80,plain,
! [X3,X0,X1] :
( element(sK13(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f81,plain,
! [X3,X0,X1] :
( sK12(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f82,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f83,plain,
! [X3,X0,X1,X4,X5] :
( in(X3,sK11(X0,X1))
| ~ in(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ element(X5,powerset(the_carrier(X0)))
| X3 != X5
| ~ closed_subset(X5,X0)
| ~ subset(X1,X3)
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f54]) ).
fof(f88,plain,
! [X2] :
( ~ in(sK4(X2),powerset(the_carrier(sK2)))
| ~ element(sK4(X2),powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(X2),sK2)
| ~ subset(sK3,sK4(X2))
| ~ in(sK4(X2),X2) ),
inference(equality_resolution,[],[f64]) ).
fof(f89,plain,
! [X0,X1,X4,X5] :
( in(X4,sK11(X0,X1))
| ~ in(X4,powerset(the_carrier(X0)))
| ~ element(X5,powerset(the_carrier(X0)))
| X4 != X5
| ~ closed_subset(X5,X0)
| ~ subset(X1,X4)
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(equality_resolution,[],[f83]) ).
fof(f90,plain,
! [X0,X1,X5] :
( in(X5,sK11(X0,X1))
| ~ in(X5,powerset(the_carrier(X0)))
| ~ element(X5,powerset(the_carrier(X0)))
| ~ closed_subset(X5,X0)
| ~ subset(X1,X5)
| sP1(X0,X1)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(equality_resolution,[],[f89]) ).
fof(f91,plain,
! [X0] :
( subset(sK3,sK5(X0))
| in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(superposition,[],[f59,f61]) ).
fof(f95,plain,
! [X0] :
( ~ in(sK5(X0),powerset(the_carrier(sK2)))
| ~ element(sK5(X0),powerset(the_carrier(sK2)))
| ~ closed_subset(sK5(X0),sK2)
| ~ subset(sK3,sK5(X0))
| ~ in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(superposition,[],[f88,f61]) ).
fof(f96,plain,
! [X0] :
( ~ in(sK5(X0),powerset(the_carrier(sK2)))
| ~ closed_subset(sK5(X0),sK2)
| ~ subset(sK3,sK5(X0))
| ~ in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f95,f62]) ).
fof(f97,plain,
! [X0] :
( ~ in(sK5(X0),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(X0))
| ~ in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f96,f60]) ).
fof(f160,plain,
! [X0,X1] :
( sK6(X0,X1) != sK8(X0,X1)
| ~ sP1(X0,X1)
| ~ sP1(X0,X1) ),
inference(superposition,[],[f72,f71]) ).
fof(f163,plain,
! [X0,X1] :
( sK6(X0,X1) != sK8(X0,X1)
| ~ sP1(X0,X1) ),
inference(duplicate_literal_removal,[],[f160]) ).
fof(f164,plain,
! [X0,X1] : ~ sP1(X0,X1),
inference(forward_subsumption_resolution,[],[f163,f66]) ).
fof(f170,plain,
! [X3,X0,X1] :
( ~ in(X3,sK11(X0,X1))
| subset(X1,X3)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f77,f164]) ).
fof(f171,plain,
! [X3,X0,X1] :
( closed_subset(sK13(X0,X1,X3),X0)
| ~ in(X3,sK11(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f78,f164]) ).
fof(f175,plain,
! [X3,X0,X1] :
( sK13(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f79,f164]) ).
fof(f176,plain,
! [X2,X0,X1] :
( closed_subset(X0,X1)
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(superposition,[],[f171,f175]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ in(X0,sK11(X1,X2))
| closed_subset(X0,X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(duplicate_literal_removal,[],[f176]) ).
fof(f178,plain,
! [X3,X0,X1] :
( sK12(X0,X1,X3) = X3
| ~ in(X3,sK11(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f81,f164]) ).
fof(f179,plain,
! [X3,X0,X1] :
( element(sK13(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f80,f164]) ).
fof(f180,plain,
! [X2,X0,X1] :
( element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(superposition,[],[f179,f175]) ).
fof(f181,plain,
! [X2,X0,X1] :
( element(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f182,plain,
! [X3,X0,X1] :
( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
| ~ in(X3,sK11(X0,X1))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f82,f164]) ).
fof(f188,plain,
! [X2,X0,X1] :
( in(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(superposition,[],[f182,f178]) ).
fof(f189,plain,
! [X2,X0,X1] :
( in(X0,powerset(the_carrier(X1)))
| ~ in(X0,sK11(X1,X2))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(duplicate_literal_removal,[],[f188]) ).
fof(f191,plain,
! [X0,X1] :
( ~ in(sK4(X0),sK11(sK2,X1))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ element(sK4(X0),powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(X0),sK2)
| ~ subset(sK3,sK4(X0))
| ~ in(sK4(X0),X0) ),
inference(resolution,[],[f189,f88]) ).
fof(f193,plain,
! [X0,X1] :
( ~ in(sK5(X0),sK11(sK2,X1))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(X0))
| ~ in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(resolution,[],[f189,f97]) ).
fof(f197,plain,
! [X0,X1] :
( ~ in(sK5(X0),sK11(sK2,X1))
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(X0))
| ~ in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f193,f58]) ).
fof(f198,plain,
! [X0,X1] :
( ~ in(sK4(X0),sK11(sK2,X1))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ element(sK4(X0),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(X0))
| ~ in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f191,f177]) ).
fof(f199,plain,
! [X0,X1] :
( ~ in(sK5(X0),sK11(sK2,X1))
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(X0))
| ~ in(sK5(X0),X0)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f197,f57]) ).
fof(f200,plain,
! [X0,X1] :
( ~ in(sK4(X0),sK11(sK2,X1))
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ element(sK4(X0),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(X0))
| ~ in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f198,f58]) ).
fof(f201,plain,
! [X0,X1] :
( ~ in(sK4(X0),sK11(sK2,X1))
| ~ element(X1,powerset(the_carrier(sK2)))
| ~ element(sK4(X0),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(X0))
| ~ in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f200,f57]) ).
fof(f202,plain,
! [X0,X1,X5] :
( in(X5,sK11(X0,X1))
| ~ in(X5,powerset(the_carrier(X0)))
| ~ element(X5,powerset(the_carrier(X0)))
| ~ closed_subset(X5,X0)
| ~ subset(X1,X5)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(forward_subsumption_resolution,[],[f90,f164]) ).
fof(f203,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(factoring,[],[f199]) ).
fof(f215,plain,
! [X0] :
( ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(factoring,[],[f201]) ).
fof(f220,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| subset(X0,sK4(sK11(sK2,X0)))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X0,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f203,f170]) ).
fof(f223,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| subset(X0,sK4(sK11(sK2,X0)))
| ~ topological_space(sK2)
| ~ top_str(sK2) ),
inference(duplicate_literal_removal,[],[f220]) ).
fof(f226,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| subset(X0,sK4(sK11(sK2,X0)))
| ~ top_str(sK2) ),
inference(forward_subsumption_resolution,[],[f223,f58]) ).
fof(f229,plain,
! [X0] :
( ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| subset(X0,sK4(sK11(sK2,X0))) ),
inference(forward_subsumption_resolution,[],[f226,f57]) ).
fof(f244,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X0,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f215,f202]) ).
fof(f246,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ topological_space(sK2)
| ~ top_str(sK2) ),
inference(duplicate_literal_removal,[],[f244]) ).
fof(f248,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ top_str(sK2) ),
inference(forward_subsumption_resolution,[],[f246,f58]) ).
fof(f249,plain,
! [X0] :
( ~ in(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0))) ),
inference(forward_subsumption_resolution,[],[f248,f57]) ).
fof(f259,plain,
! [X0] :
( ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(resolution,[],[f249,f63]) ).
fof(f264,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f259,f59]) ).
fof(f272,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(resolution,[],[f264,f215]) ).
fof(f277,plain,
! [X0] :
( in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ closed_subset(sK5(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(sK5(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(superposition,[],[f264,f61]) ).
fof(f281,plain,
! [X0] :
( ~ element(sK4(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0))) ),
inference(duplicate_literal_removal,[],[f272]) ).
fof(f282,plain,
! [X0] :
( in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(sK5(sK11(sK2,X0)),powerset(the_carrier(sK2)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f277,f60]) ).
fof(f283,plain,
! [X0] :
( in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(forward_subsumption_resolution,[],[f282,f62]) ).
fof(f284,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(resolution,[],[f283,f199]) ).
fof(f296,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ in(sK5(sK11(sK2,X0)),sK11(sK2,X0)) ),
inference(duplicate_literal_removal,[],[f284]) ).
fof(f298,plain,
! [X0] :
( in(sK4(sK11(sK2,X0)),sK11(sK2,X0))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0))) ),
inference(forward_subsumption_resolution,[],[f296,f283]) ).
fof(f304,plain,
! [X0] :
( ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| subset(X0,sK4(sK11(sK2,X0)))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X0,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f298,f170]) ).
fof(f307,plain,
! [X0] :
( ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| subset(X0,sK4(sK11(sK2,X0)))
| ~ topological_space(sK2)
| ~ top_str(sK2) ),
inference(duplicate_literal_removal,[],[f304]) ).
fof(f312,plain,
! [X0] :
( ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| subset(X0,sK4(sK11(sK2,X0)))
| ~ top_str(sK2) ),
inference(forward_subsumption_resolution,[],[f307,f58]) ).
fof(f314,plain,
! [X0] :
( subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ subset(X0,sK5(sK11(sK2,X0))) ),
inference(forward_subsumption_resolution,[],[f312,f57]) ).
fof(f348,plain,
! [X0,X1] :
( ~ closed_subset(sK4(sK11(sK2,X0)),sK2)
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f281,f181]) ).
fof(f352,plain,
! [X0,X1] :
( ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f348,f177]) ).
fof(f353,plain,
! [X0,X1] :
( ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| ~ top_str(sK2)
| ~ element(X1,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f352,f58]) ).
fof(f354,plain,
! [X0,X1] :
( ~ in(sK4(sK11(sK2,X0)),sK11(sK2,X1))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X1,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f353,f57]) ).
fof(f370,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK5(sK11(sK2,X0))) ),
inference(resolution,[],[f354,f298]) ).
fof(f378,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ subset(X0,sK4(sK11(sK2,X0)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ subset(sK3,sK5(sK11(sK2,X0))) ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f381,plain,
! [X0] :
( ~ subset(sK3,sK5(sK11(sK2,X0)))
| ~ subset(sK3,sK4(sK11(sK2,X0)))
| ~ subset(X0,sK5(sK11(sK2,X0)))
| ~ element(X0,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f378,f314]) ).
fof(f384,plain,
( ~ subset(sK3,sK5(sK11(sK2,sK3)))
| ~ subset(sK3,sK4(sK11(sK2,sK3)))
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(factoring,[],[f381]) ).
fof(f385,plain,
( ~ subset(sK3,sK5(sK11(sK2,sK3)))
| ~ subset(sK3,sK4(sK11(sK2,sK3))) ),
inference(forward_subsumption_resolution,[],[f384,f56]) ).
fof(f386,plain,
( ~ subset(sK3,sK4(sK11(sK2,sK3)))
| in(sK5(sK11(sK2,sK3)),sK11(sK2,sK3))
| in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)) ),
inference(resolution,[],[f385,f91]) ).
fof(f387,plain,
( in(sK5(sK11(sK2,sK3)),sK11(sK2,sK3))
| in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)) ),
inference(forward_subsumption_resolution,[],[f386,f59]) ).
fof(f391,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ subset(sK3,sK5(sK11(sK2,sK3)))
| ~ element(sK3,powerset(the_carrier(sK2)))
| subset(sK3,sK4(sK11(sK2,sK3))) ),
inference(resolution,[],[f387,f229]) ).
fof(f393,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| subset(sK3,sK5(sK11(sK2,sK3)))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f387,f170]) ).
fof(f396,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| subset(sK3,sK5(sK11(sK2,sK3)))
| ~ top_str(sK2)
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f393,f58]) ).
fof(f397,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ subset(sK3,sK5(sK11(sK2,sK3)))
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f391,f385]) ).
fof(f400,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| subset(sK3,sK5(sK11(sK2,sK3)))
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f396,f57]) ).
fof(f401,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| ~ subset(sK3,sK5(sK11(sK2,sK3))) ),
inference(forward_subsumption_resolution,[],[f397,f56]) ).
fof(f403,plain,
( in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3))
| subset(sK3,sK5(sK11(sK2,sK3))) ),
inference(forward_subsumption_resolution,[],[f400,f56]) ).
fof(f424,plain,
in(sK4(sK11(sK2,sK3)),sK11(sK2,sK3)),
inference(forward_subsumption_resolution,[],[f403,f401]) ).
fof(f426,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,sK3)))
| ~ subset(sK3,sK4(sK11(sK2,sK3)))
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f424,f354]) ).
fof(f430,plain,
( subset(sK3,sK4(sK11(sK2,sK3)))
| ~ topological_space(sK2)
| ~ top_str(sK2)
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(resolution,[],[f424,f170]) ).
fof(f434,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| ~ subset(sK3,sK4(sK11(sK2,sK3))) ),
inference(duplicate_literal_removal,[],[f426]) ).
fof(f435,plain,
( subset(sK3,sK4(sK11(sK2,sK3)))
| ~ top_str(sK2)
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f430,f58]) ).
fof(f438,plain,
~ subset(sK3,sK4(sK11(sK2,sK3))),
inference(forward_subsumption_resolution,[],[f434,f56]) ).
fof(f440,plain,
( subset(sK3,sK4(sK11(sK2,sK3)))
| ~ element(sK3,powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f435,f57]) ).
fof(f442,plain,
subset(sK3,sK4(sK11(sK2,sK3))),
inference(forward_subsumption_resolution,[],[f440,f56]) ).
fof(f448,plain,
$false,
inference(forward_subsumption_resolution,[],[f442,f438]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU314+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 28 04:38:37 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.18/1.15 % (4153521)Detected formulas, will run a generic FOF schedule.
% 1.18/1.15 % (4153536)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1369084740:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.18/1.15 % (4153536)First to succeed.
% 1.18/1.15 % (4153536)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4153521"
% 1.18/1.15 % (4153537)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2771948354:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.18/1.15 % (4153535)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=466752708:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.18/1.15 % (4153534)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1303692671:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.18/1.15 % (4153532)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=562553669:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.18/1.15 % (4153533)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3866414715:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.18/1.15 % (4153537)Also succeeded, but the first one will report.
% 1.18/1.15 % (4153538)dis-21_1_sil=8000:lcm=predicate:random_seed=599249681:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.18/1.15 % (4153535)Refutation not found, incomplete strategy
% 1.18/1.15 % (4153535)------------------------------
% 1.18/1.15 % (4153535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.18/1.15 % (4153535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/1.15 % (4153535)CaDiCaL version: 2.1.3
% 1.18/1.15 % (4153535)Termination reason: Refutation not found, incomplete strategy
% 1.18/1.15 % (4153535)Time elapsed: 0.006 s
% 1.18/1.15 % (4153535)Peak memory usage: 88 MB
% 1.18/1.15 % (4153535)Instructions burned: 4 (million)
% 1.18/1.15 % (4153538)Instruction limit reached!
% 1.18/1.15 % (4153538)------------------------------
% 1.18/1.15 % (4153538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.18/1.15 % (4153538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.18/1.15 % (4153538)CaDiCaL version: 2.1.3
% 1.18/1.15 % (4153538)Termination reason: Instruction limit
% 1.18/1.15 % (4153538)Termination phase: Saturation
% 1.18/1.15 % (4153538)Time elapsed: 0.098 s
% 1.18/1.15 % (4153538)Peak memory usage: 89 MB
% 1.18/1.15 % (4153538)Instructions burned: 130 (million)
% 1.18/1.15 % (4153536)Refutation found. Thanks to Tanya!
% 1.18/1.15 % SZS status Theorem for theBenchmark
% 1.18/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.49 % (4153536)------------------------------
% 3.36/1.49 % (4153536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.49 % (4153536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.49 % (4153536)CaDiCaL version: 2.1.3
% 3.36/1.49 % (4153536)Termination reason: Refutation
% 3.36/1.49 % (4153536)Time elapsed: 0.013 s
% 3.36/1.49 % (4153536)Peak memory usage: 88 MB
% 3.36/1.49 % (4153536)Instructions burned: 23 (million)
% 3.36/1.49 % (4153536)------------------------------
% 3.36/1.49 % (4153536)------------------------------
% 3.36/1.49 % (4153521)Success in time 0.379 s
% 3.36/1.49 % Vampire exiting
%------------------------------------------------------------------------------